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Robotica: decoupled elastostatic stiffness modeling of hybrid robots

Published online by Cambridge University Press:  24 May 2024

Baoyu Wang Open the ORCID record for Baoyu Wang [Opens in a new window] ,
Peixing Li ,
Chao Yang Open the ORCID record for Chao Yang [Opens in a new window] ,
Xudong Hu  and
Yanzheng Zhao
Baoyu Wang
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, China
Peixing Li
Affiliation:
School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China
Chao Yang
Affiliation:
College of Mechanical and Electrical Engineering, Jiaxing University, Jiaxing, China
Xudong Hu*
Affiliation:
School of Mechanical Engineering, Zhejiang Sci-Tech University, Hangzhou, China
Yanzheng Zhao*
Affiliation:
Research Institute of Robotics, Shanghai Jiao Tong University, Shanghai, China
*
Corresponding authors: Xudong Hu; Email: xdhu@zstu.edu.cn, Yanzheng Zhao; Email: yzh-zhao@sjtu.edu.cn
Corresponding authors: Xudong Hu; Email: xdhu@zstu.edu.cn, Yanzheng Zhao; Email: yzh-zhao@sjtu.edu.cn
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Abstract

A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano’s second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism’s stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano’s second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach.

Keywords

hybrid robotstiffnessstrain energyscrew theory
Type
Research Article
Information
Robotica , First View , pp. 1 - 19
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Wu, J., Li, T., Wang, J. and Wang, L., “Stiffness and natural frequency of a 3-DOF parallel manipulator with consideration of additional leg candidates,” Robot Auton Syst 61(8), 868–875 (2013).CrossRefGoogle Scholar
Wu, J., Ye, H., Yu, G. and Huang, T., “A novel dynamic evaluation method and its application to a 4-DOF parallel manipulator,” Mech Mach Theory 168, 104627 (2022).CrossRefGoogle Scholar
Wu, J., Gao, Y., Zhang, B. and Wang, L., “Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment,” Robot Comp-Integ Manuf 44, 199–207 (2017).CrossRefGoogle Scholar
Zhang, J., Zhao, Y. and Jin, Y., “Kinetostatic-model-based stiffness analysis of exechon PKM,” Robot Comp-Integr Manuf 37, 208–220 (2016).CrossRefGoogle Scholar
Shen, H. P., Zhu, Z. Q. and Meng, Q. M., “Kinematics and stiffness modeling analysis of spatial 2T1R parallel mechanism with zero coupling degree,” Trans Chin Soc Ag Mach 51(10), 411–420 (2020).Google Scholar
Kim, H. S. and Lipkin, H., “Stiffness of parallel manipulators with serially connected legs,” J Mech Robot 6(3), 031001 (2014).Google Scholar
Pashkevich, A., Klimchik, A. and Chablat, D., “Enhanced stiffness modeling of manipulators with passive joints,” Mech Mach Theory 46(5), 662–679 (2011).CrossRefGoogle Scholar
Taghvaeipour, A., Angeles, J. and Lessard, L., “On the elastostatic analysis of mechanical systems,” Mech Mach Theory 58(3), 202–216 (2012).CrossRefGoogle Scholar
Huang, Z., Zhao, Y. and Liu, J. F., “Kinetostatic analysis of 4-R(CRR) parallel manipulator with overconstraints via reciprocal-screw theory,” Adv Mech Eng 2, 404960 (2010).CrossRefGoogle Scholar
Hu, B., “Kinematically identical manipulators for the exechon parallel manipulator and their comparison study,” Mech Mach Theory 103, 117–137 (2016).CrossRefGoogle Scholar
Wang, S.-C., Hikita, H., Kubo, H., Zhao, Y.-S., Huang, Z. and Ifukube, T., “Kinematics and dynamics of a 6 degree-of-freedom fully parallel manipulator with elastic joints,” Mech Mach Theory 38(5), 439–461 (2003).CrossRefGoogle Scholar
Xu, Y., Yao, J. and Zhao, Y., “Inverse dynamics and internal forces of the redundantly actuated parallel manipulators,” Mech Mach Theory 51, 172–184 (2012).CrossRefGoogle Scholar
Lu, Y., Chen, L., Wang, P., Zhang, B., Zhao, Y. S. and Hu, B., “Statics and stiffness analysis of a novel six-component force/torque sensor with 3-RPPS compliant parallel structure,” Mech Mach Theory 62, 99–111 (2013).CrossRefGoogle Scholar
Xu, Y., Liu, W., Yao, J. and Zhao, Y., “A method for force analysis of the overconstrained lower mobility parallel mechanism,” Mech Mach Theory 88, 31–48 (2015).CrossRefGoogle Scholar
Enferadi, J. and Tootoonchi, A. A., “Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator,” Robotica 29(2), 193–209 (2011).CrossRefGoogle Scholar
Rezaei, A., Akbarzadeh, A. and Akbarzadeh-T., M.-R., “An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form,” Mech Mach Theory 51, 195–216 (2012).CrossRefGoogle Scholar
Rezaei, A. and Akbarzadeh, A., “Position and stiffness analysis of a new asymmetric 2PRRPPR parallel CNC machine,” Adv Robot 27(2), 133–145 (2013).CrossRefGoogle Scholar
Yan, S. J., Ong, S. K. and Nee, A. Y. C., “Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method,” Robot Comp-Int Manuf 37, 13–22 (2016).CrossRefGoogle Scholar
Li, C. Y. Q. C., Chen, Q. H. and Xu, L. M., “Elastostatic stiffness modeling of overconstrained parallel manipulators,” Mech Mach Theory 112, 58–74 (2018).Google Scholar
Yang, C., Chen, Q., Tong, J. and Li, Q., “Elastostatic stiffness analysis of a 2PUR-PSR overconstrained parallel mechanism,” Int J Precis Eng Manuf 20(4), 569–581 (2019).CrossRefGoogle Scholar
Yang, C., Li, Q. and Chen, Q., “Decoupled elastostatic stiffness modeling of parallel manipulators based on the rigidity principle,” Mech Mach Theory 145, 103718 (2020).CrossRefGoogle Scholar
Klimchik, A., Pashkevich, A. and Chablat, D., “Fundamentals of manipulator stiffness modeling using matrix structural analysis,” Mech Mach Theory 133, 365–394 (2019).CrossRefGoogle Scholar
Klimchik, A., Chablat, D. and Pashkevich, A., “Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings,” Mech Mach Theory 79, 1–28 (2014).CrossRefGoogle Scholar
Zhao, C., Guo, H., Zhang, D., Liu, R., Li, B. and Deng, Z., “Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis,” Mech Mach Theory 152, 103960 (2020).CrossRefGoogle Scholar
Yu, G., Wu, J. and Wang, L., “Stiffness model of a 3-DOF parallel manipulator with two additional legs,” Int J Adv Robot Syst 11(10), 173 (2014).CrossRefGoogle Scholar
Cammarata, A., “Unified formulation for the stiffness analysis of spatial mechanisms,” Mech Mach Theory 105, 272–284 (2016).CrossRefGoogle Scholar
Cammarata, A., Condorelli, D. and Sinatra, R., “An algorithm to study the elastodynamics of parallel kinematic machines with lower kinematic pairs,” J Mech Robot 5(1), 011004 (2012).CrossRefGoogle Scholar
Wu, J., Wang, J., Wang, L., Li, T. and You, Z., “Study on the stiffness of a 5-DOF hybrid machine tool with actuation redundancy,” Mech Mach Theory 44(2), 289–305 (2009).CrossRefGoogle Scholar
Deblaise, D., Hernot, X. and Maurine, P., “A Systematic Analytical Method for PKM Stiffness Matrix Calculation,” In: IEEE International Conference on Robotics & Automation, (2006) pp. 4213–4219.Google Scholar
Ball, R. A.. Treatise on the Theory of Screws (Cambridge University Press, England, 1900). pp. 1–30.Google Scholar
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